(57) An easy method of forming purified carbon nanotubes from which graphitic phase or carbon particles are removed, using a high-density plasma. Carbon nanotubes are grown on a substrate using a plasma chemical vapor deposition method at a high plasma density of 10¹¹ cm^-3 or more. The carbon nanotube formation includes: growing a carbon nanotube layer on a substrate to have a predetermined thickness by plasma deposition; purifying the carbon nanotube layer by plasma etching; and repeating the growth and the purification of the carbon nanotube layer. For the plasma etching, a halogen-containing gas, for example, a carbon tetrafluoride gas, is #used as a source gas.